15 problems

Let $G$ be a finite $p$-group, where $p$ is prime. The Schur multiplier exponent conjecture. … This conjecture strengthens the known bound suggested by the counterexamples to Schur…

Let $G$ be a finite $p$-group, where $p$ is prime. Write $\operatorname{exp}(G)$ for the exponent of $G$, and let $H_2(G,\mathbb{Z})$ be its second homology group with integer coef…

Let $G$ be a finite group. Write $\operatorname{exp}(G)$ for the exponent of $G$, and let $H_2(G,\mathbb{Z})$ be its second homology group with integer coefficients. Moravec's squa…

Let $G$ be a finite $p$-group, where $p$ is prime. Exponent conjecture for finite $p$-groups. … This is attributed to the authors of and gives a bound for the exponent of the Schur…

Let $G$ be a finite group, and let $H_2(G,\mathbb{Z})$ denote its Schur multiplier. Exponent-square conjecture. … This conjecture was proposed as a proposed replacement for Schur's…

Let $G$ be a finite $p$-group, and write $M(G)=H_2(G,\mathbb{Z})$ for its Schur multiplier. Write $\operatorname{exp}(G)$ for the exponent of $G$. Exponent conjecture for finite…

Partial Schur multiplier conjecture. Every component of the partial Schur multiplier of $G$ is isomorphic to a direct product of copies of $\mathbb K^\times$.

Equidistribution conjecture. As $N\to\infty$, the values of $\mathfrak{z}(\rho)$ for those extensions whose discriminant norm lies in $[-N,N]$ are equidistributed over…

Let $\Gamma_d$ be a Fabrykowski–Gupta group with $d$ prime, and let $M(G)$ denote a Schur multiplier. Fabrykowski–Gupta conjecture. The Schur multiplier of $\Gamma_d$, modulo the D…

Let $\Delta$ be the Basilica group, let $M_c(\Delta)$ be its $c$-th Dwyer quotient, and let $\mathcal A_\ell(c)$ be the abelian groups specified below. Dwyer quotient conjecture. ……

Let $\tilde{\mathfrak G}$ be the Grigorchuk super-group, and let $M_c(\tilde{\mathfrak G})$ denote its $c$-th Dwyer quotient. Dwyer quotient conjecture. … with $m\in\mathbb N$. The…

Let $\bar{\mathfrak G}$ be the twisted twin of the Grigorchuk group, and let $M_c(\bar{\mathfrak G})$ denote its $c$-th Dwyer quotient. Dwyer quotient conjecture. … with…

Let ${\mathfrak G}$ be the Grigorchuk group, and let $M_c({\mathfrak G})$ denote its $c$-th Dwyer quotient. Dwyer quotient conjecture. … with $m\in{\mathbb N}_0$. The conjecture pr…

Let $G$ be a group with a free presentation $F/R$. The $c$-nilpotent multiplier of $G$ is … For $c=1$, write $M(G)=M^{(1)}(G)$ for the Schur multiplier. If $G$ is a finite $p$-grou…

Let $G$ be a finite $p$-group, let $M(G)$ denote its Schur multiplier, and let $\exp(H)$ denote the exponent of a group $H$. Exponent conjecture for Schur multipliers. The exponent…